This application claims Paris Convention priority of German patent application number 100 35 319.3 filed on Jul. 18, 2000, the complete disclosure of which is hereby incorporated by reference.
The invention concerns a method of NMR spectroscopy or nuclear magnetic resonance tomography, wherein a sequence of temporally offset radio frequency pulses is applied onto a spin ensemble, at least one of which is designed as refocusing pulse.
In the following, reference is made to the accompanying literature list (xe2x80x9cDxe2x80x9d and corresponding numbers in round brackets).
A nuclear magnetic resonance signal is frequently measured by means of the spin echo method known from (D1). The excited magnetization is thereby after a period te/2 submitted to a refocusing pulse and a spin echo is formed after a further time period te/2. At the time of the spin echo, effects acting on the spins, such as chemical shift, susceptibility, field inhomogeneity, are refocused such that all spins have a coherent signal phase with respect to these effects. The signal maximum is achieved if the flip angle of the refocusing pulse is exactly 180xc2x0. In practice, such an ideal flip angle can only approximately be realized such that, in particular with methods based on formation of many spin echos, one obtains signal losses due to deviation of the flip angle of the refocusing pulses by 180xc2x0.
Such a deviation can occur either through technical facts or be artificially produced, e.g. in applications on human beings for keeping the values of the radiated radio frequency energy within tolerable limits (SAR=specific absorption rate). Literature proposed a series of measures for limiting the corresponding signal losses. This includes on the one hand the so-called Carr-Purrcell-Meiboom-Gill method (D2) wherein by an appropriate displacement of the pulse phase between excitation and refocusing pulses, partial automatic compensation of the refocusing pulses is effected.
It could be shown that with such a sequence with long echo trains, high echo amplitudes could be achieved (D3) even with small refocusing flip angles.
When using different flip angles across the first refocusing periods of the multi-echo train, the echo amplitude can be further increased (D4)(D5).
In applications of analytical NMR spectroscopy, improvements through different phase cycles such as MLEV16 or XY16 are used (D6). These serve mainly for compensating residual small errors in refocusing pulses with a flip angle of approximately 180xc2x0.
All methods known from literature include that in case of deviation of the flip angle of only one single refocusing pulse by 180xc2x0, signal loss occurs which can, at best, be reduced through corresponding design of the subsequent refocusing pulses.
In contrast thereto, it is the object of the present invention to present a method for reversing the occurred signal losses even after application of refocusing pulses of any flip angle, and reproduce the complete signal amplitude with respect to dephasing through chemical shift, susceptibility and field inhomogeneity.
In accordance with the invention, this object is achieved in a effective manner in that after a sequence of pulses with flip angles xcex11 . . . xcex1n (with xcex11 . . . xcex1nxe2x89xa70 xc2x0) and phases xcfx861 . . . xcfx86n between which spins are dephased by xcfx861 . . . xcfx86n, a central refocusing pulse is applied as (n+1)th pulse, followed by a pulse sequence which is mirror-symmetrical to the central refocusing pulse, wherein the flip angles xcex1n+2 . . . xcex12n+1 and phases xcfx86n+2 . . . xcfx862n+1 of the pulses have, in comparison with the corresponding pulses with xcex1n . . . xcex11 and xcfx86n . . . xcfx861, a negative sign with respect to amplitude and phase and the dephasings xcfx86n+2 . . . xcfx862n+1 which are also mirror-symmetrical to the central refocusing pulse in the sequence are equal to the mirror-symmetrical dephasings xcfx86n . . . xcfx861 such that at the end of the pulse sequence, an output magnetization MA(Mx,My,Mz) of the spin ensemble is transferred with respect to the central refocusing pulse through application of rotation corresponding to the symmetrical relation
MR(xe2x88x92Mx,My,xe2x88x92Mz)=Roty(180xc2x0)*MA(Mx,My,Mz)
into a final magnetization MR=(xe2x88x92Mx,My,xe2x88x92Mz) and thereby refocused neglecting relaxation effects.
Refocusing, effected by the inventive pulse sequence, of the initial magnetization MA is characterized as hyper echo formation.
Method
The main idea is based on the observations of symmetry relations with respect to vector rotation: We observe rotations of vectors which hold:
Rotation about the z axis by an angle xcfx86:                                           Rot            z                    ⁡                      (                          ϕ              n                        )                          =                  "LeftBracketingBar"                                                                      cos                  ⁡                                      (                                          ϕ                      n                                        )                                                                                                sin                  ⁡                                      (                                          ϕ                      n                                        )                                                                              0                                                                                      -                                      sin                    ⁡                                          (                                              ϕ                        n                                            )                                                                                                                    cos                  ⁡                                      (                                          ϕ                      n                                        )                                                                              0                                                                    0                                            0                                            1                                              "RightBracketingBar"                                    [1]            
Rotation about the y axis by an angle xcex1:                                           Rot            y                    ⁡                      (                          α              n                        )                          =                  "LeftBracketingBar"                                                                      cos                  ⁡                                      (                                          α                      n                                        )                                                                              0                                                              -                                      sin                    ⁡                                          (                                              α                        n                                            )                                                                                                                          0                                            1                                            0                                                                                      sin                  ⁡                                      (                                          α                      n                                        )                                                                              0                                                              cos                  ⁡                                      (                                          α                      n                                        )                                                                                "RightBracketingBar"                                    [2]            
Rotation Rotxcfx86(xcex1) about a rotary axis which is tilted in the x-y plane about an angle xcfx86 with respect to the y axis can be described as:
Rotxcfx86(xcex1)=Rotz(xcfx86n)Roty(xcex1n)Rotz(xe2x88x92xcfx86n)xe2x80x83xe2x80x83[3]
Corresponding to the conventions of the matrix multiplication, calculation is effected from the right to the left.
Observation of two vectors V(x,y,z) and V*(xe2x88x92x,y,xe2x88x92v) which are disposed symmetrically with respect to rotation about 180xc2x0 about the y axis, facilitates representation (FIGS. 1A-1c):
L1: Rotation Rotz(xcfx86) of a vector V(x,y,z) about the z axis at an angle xcfx86 produces the resulting vector Vxe2x80x2(xxe2x80x2,yxe2x80x2,z). For a vector V*(xe2x88x92x,y,xe2x88x92z) rotated with respect to V about the y axis by 180xc2x0, the point V*xe2x80x2(xe2x88x92xxe2x80x2,yxe2x80x2,xe2x88x92z) corresponding to Vxe2x80x2 results from V* through rotation. by xe2x88x92xcfx86 (FIG. 1A).
Accordingly V can be transferred by rotation about z with a turning angle of xcfx86, subsequent rotation about y with a turning angle of 180xc2x0 and subsequent rotation about z with xcfx86 in V*:
V*(xe2x88x92x, y, xe2x88x92z)=Rotz(xcfx86)*Roty(180xc2x0)*Rotz(xcfx86)*V(x, y, z)=Roty(180xc2x0)V(x, y, z).xe2x80x83xe2x80x83[4]
L2: Rotation Roty(xcex1) of V about the y axis by an angle xcex1 generates the resulting vector Vxe2x80x2(xxe2x80x2,y,zxe2x80x2). The corresponding symmetrical point V*xe2x80x2(xe2x88x92xxe2x80x2,yxe2x80x2,xe2x88x92z) also results from V* through rotation by xcex1.
A trivial addition of the turning angle (FIG. 1B) thus obtains:
V*(xe2x88x92x, y, xe2x88x92z)=Roty(xcex1)*Roty(180xc2x0)*Roty(xe2x88x92xcex1)*V(x, y, z)=Roty(180xc2x0)V(x, y, z).xe2x80x83xe2x80x83[5]
From L1 and L2 together with equation [3] one obtains:
L3: Rotation Rotxcfx86(xcex1) by an angle xcex1, of V about an axis, tilted with respect to the y axis by xcfx86 produces the resulting vector Vxe2x80x2(xxe2x80x2,y,zxe2x80x2). The corresponding symmetrical point V*xe2x80x2(xe2x88x92xxe2x80x2,yxe2x80x2,xe2x88x92z) results from V* through rotation Rotxcfx86 (xcex1) about a rotational axis tilted with respect to the y axis by xe2x88x92xcfx86. Therefore (FIG. 1C):
V*(xe2x88x92x, y, xe2x88x92z)=Rotxcfx86(xe2x88x92xcex1)*Roty(180xc2x0)*Rotxcfx86(xcex1)*V(x, y, z)
And with equations [3]-[5]:
V*(xe2x88x92x, y, xe2x88x92z)=Rotz(xcfx86n)*Roty(xe2x88x92xcex1n)*Rotz(xe2x88x92xcfx86n)*Roty(180xc2x0)*Rotz(xe2x88x92xcfx86n)*Roty(xcex1n) *Rotz(xcfx86n)*V(x, y, vz)=Roty(180xc2x0)V(x, y, z).xe2x80x83xe2x80x83[6]
Rotation with xe2x88x92xcex1 about an axis xe2x88x92xcfx86 corresponds to rotation with xcex1 about 180xc2x0xe2x88x92xcfx86:
Rotxcfx86(xe2x88x92xcex1)=Rot180 xc2x0xe2x88x92xcfx86(xcex1)xe2x80x83xe2x80x83[7]
Both nomenclatures are equivalent and are used in the following depending on their practicability.
These initially purely mathematical symmetrical relations can be converted into pulse sequences of NMR spectroscopy or MR tomography. Equation [4] is the basis of the spin echo experiment by Hahn, which says:
Dephasing Rotz(xcfx86), applied to magnetization MA(xe2x88x92Mx,My,xe2x88x92Mz), defined as             M      A        ⁡          (              Mx        ,        My        ,        Mz            )        =      "LeftBracketingBar"                            Mx                                      My                                      Mz                      "RightBracketingBar"  
and subsequent refocusing by a 180xc2x0 pulse Roty(180xc2x0) and further phase development corresponding to Rotz(xcfx86) produces magnetization MR(xe2x88x92Mx,My,xe2x88x92Mz) which is rotationally symmetrical with respect to MA.
Corresponding to equation [4] thus results:
MR(xe2x88x92Mx,MY,xe2x88x92Mz)=Rotz(xcfx86)*Roty(180xc2x0)*Rotz(xcfx86)*MA(xe2x88x92Mx,My,xe2x88x92Mz)=Roty(180xc2x0)*MA(Mx,My,Mz)xe2x80x83xe2x80x83[8]
which means that spins are refocused by a 180xc2x0 pulse independent of their phase development xcfx86.
The phase development about xcfx86 can thereby be effected either through temporally constant mechanisms such as chemical shift, inhomogeneities etc., wherein dephasing is then characterized by an off resonance frequency xcfx89 and xcfx86 becomes proportional to the respective time intervals corresponding to xcfx86=xcfx89. xcfx86 may also be determined through variables such as magnetic field gradients or movement in inhomogeneous fields. In terms of NMR, the rotation about a rotational axis in the x-y plane described in equations [5]-[7] corresponds to application of a radio frequency pulse with flip angle xcex1.
Starting from the spin echo sequence corresponding to [8] same can be symmetrically extended according to L1-L3, equations [4]-[7] thereby maintaining the rotational symmetry, wherein the sequence in both cases is extended either by one dephasing interval corresponding to equation [4] or a pulse corresponding to equations [5]-[7].
Usually pulse sequences in MR are represented as alternating sequence of pulses and subsequent time intervals which is also the convention followed in the following examples of implementation. All statements are, of course, also true for sequences, wherein several radio frequency pulses directly follow one another or contain several dephasing steps between 2 radio frequency pulses.
The temporal development between two pulses may be arbitrary. Decisive is merely the total dephasing between subsequent pulses. Therefore, the inventive method can be formulated as follows:
Multiple pulse sequence in NMR spectroscopy or MR tomography, wherein a sequence of 2n+1 radio frequency pulses is applied to a spin system with magnetization MA(Mx,My,Mz) is characterized in that at first n radio frequency pulses R(xcex1n, xcfx86n) are applied with respective temporal separation tn which effect rotation Rotxcfx86n(xcex1n) of the spins, wherein the spins experience, in the time intervals In between the pulses, a phase development about xcfx86n corresponding to a rotation Rotz(xcfx86n) about z, and subsequently a refocusing pulse R(xcex1n+1, xcfx86n+1)=R(180xc2x0, 0xc2x0) followed by n radio frequency pulses R(xcex1n+2,xcfx86n+2) . . . R(xcex12n+1, xcfx862n+1) in a temporally reversed order and corresponding to the relation given in equations [5]-[7]
R(xcex1n+2,xcfx86n+2) . . . R(xcex12n+1,xcfx862n+1)=R(xe2x88x92xcex1n,xe2x88x92xcfx86n) . . . R(xe2x88x92xcex11,xe2x88x92xcfx861)=R(xcex1n,180xc2x0xe2x88x92xcfx86n) . . . R(xcex11,180xc2x0xe2x88x92xcfx861)xe2x80x83xe2x80x83[9]
and
xcfx86n+1 . . . xcfx862n=xcfx86n . . . xcfx861xe2x80x83xe2x80x83[10]
thereby obtaining magnetization MR which holds:
MR(xe2x88x92Mx,My,xe2x88x92Mz)=Roty(180xc2x0)*MA(Mx,My,Mz),xe2x80x83xe2x80x83[11]
which means that the initial magnetization MAis refocused independently of xcex1n, xcfx86n and xcfx86n.
This sequence is illustrated in FIG. 2.
According to the basic principle, that radio frequency pulses having a complicated amplitude and phase profile (as used e.g. for slice selection in NMR tomography) can be represented as a sequence of short pulses with discrete flip angle, equations [9]-[11] are valid analogously also for pulse sequences with amplitude and/or phase-modulated pulses. Additionally, it should be noted that the phase of the central refocusing pulse was defined to be 0xc2x0 and does not necessarily need to correspond to the reference phase of magnetization. Coordination transformation of equations [9]-[11] corresponding to equation [3] makes the refocusing relation of equation [11] also valid for any phases of the central pulse if corresponding transformation is carried out also for the other pulses.
For a central pulse having a phase C which effects rotation corresponding to (180xc2x0,xcex6) equation [9] results in:
xe2x80x83R(xcex1n+2,xcfx86n+2) . . . R(xcex12n+1,xcfx862n+1)=R(xe2x88x92xcex1n,xe2x88x92xcfx86n+2xcex6) . . . R(xe2x88x92xcex11,xe2x88x92xcfx861+2xcex6)=R(xcex1n,180xc2x0xe2x88x92xcfx86n+2xcex6) . . . R(xcex11, 180xc2x0xe2x88x92xcfx861+2xcex6)xe2x80x83xe2x80x83[12]
For completion it should be noted that the central refocusing pulse may also have a flip angle of  less than 180xc2x0. The amplitude of the formed refocused magnetization is then correspondingly weakened.
Such a pulse sequence refocuses all spins independent of their respective and optionally different phase development and form a coherent spin echo. This refocusing process through a pulse sequence is called below hyper-echo formation.
Relaxation proceedings were not taken into consideration in this derivation which lead to relaxation-based signal attenuation.
It is possible to derive a series of realizations on the basis of known pulse sequences from the basic sequence shown in FIG. 2A. Introduction of a hyper-echo formation into an existing sequence can thereby be effected in different ways:
As shown in FIG. 2B, an existing sequence (in the present case a simple spin echo sequence having a 90xc2x0 excitation pulse and a 180xc2x0 refocusing pulse) can be modified through introduction of further pulses corresponding to equations [9]-[11] into a hyper-echo sequence. Sequences where the temporal sequence of pulses already meets the dephasing conditions for hyper-echo formation thereby require optionally only modification of the flip angle and pulse phases (see below).
FIG. 2C shows the principle of integration of the hyper-echo formation through supplementation: Any pulse sequence (in this case consisting of an excitation pulse with subsequent n radio frequency pulses) is converted to a hyperecho sequence by adding a refocusing pulse and subsequent pulses according to equations [9]-[11] to form a hyper-echo.
Finally, FIG. 2D shows application of a hyper-echo for preparing magnetization as hyper-echo which is subsequently read with any pulse sequence (in the present case a simple spin echo).
Of course, these different types of introduction of a hyper-echo can be arbitrarily combined. Formation of several hyper-echos within one sequence can also be advantageous.
Some examples of application are shown below. It must be stated that the NMR literature describes an extremely large number of different multiple pulse sequences which can only be exemplarily described below. The expert can easily apply the method of symmetrization described in equations [9]-[11] for forming a completely refocused spin echo such that the following examples do not represent a limitation but merely show the general application possibilities of the basic principle.
The following application classes seem to be advantageous:
1. Multi-echo Sequences
Application of the principle described in equation [11] to transverse magnetization recovers complete magnetizationxe2x80x94when relaxation effects are neglectedxe2x80x94(corresponding to the continuous use of refocusing pulses having a flip angle of 180xc2x0) for any values of xcex11 . . . xcex1n. While the amplitude is  less than  less than 1 after each echo produced by xcex1n, the complete amplitude is recovered after the inventive sequence.
A special case of equations [9]-[11] is given when the magnetization vector MAis oriented parallel to the central refocusing pulse R(180xc2x0). In this case MR=MA, i.e. magnetization is converted into itself (except for relaxation effects during the sequence). This is the case e.g. in the CPMG multi echo methods (D2) wherein magnetization is generated by a 90xc2x0 pulse. In the subsequent multiple refocusing, 180xc2x0 pulses are applied with a phase which is perpendicular to the excitation pulse and thus parallel to the excited magnetization.
Clinical application of such sequences often requires selection of the flip angle of the refocusing pulse  less than 180xc2x0 to limit the radio frequency output (D3). Modification of a CPMG method according to the inventive method can be realized as below:
If MA is magnetization directly after excitation and possible phase effects during the excitation pulse are neglected, the condition MA parallel to R(180xc2x0,0) is met for all subsequent refocusing pulses. For all xcfx86n thus holds:
xcfx86n=xcfx860=0.
Due to the equidistant refocusing pulses in CPMG sequences (and when using symmetrical conditions corresponding to magnetic field gradients for dephasing caused thereby) it is furthermore true for all xcfx86n:
xe2x80x83xcfx86n=xcfx861
The symmetry of the inventive sequence is achieved in this case through inversion of the respectively applied flip angles. The phases always remain zero (FIG. 3):
R(xcex1n+2,0) . . . R(xcex12n+1,0)=R(xe2x88x92xcex11,0)xe2x80x83xe2x80x83[13]
With this modification, the amplitude of the (2n+1)th echo can be reproduced to the completely refocused value (=1) for any xcex11 . . . xcex1n. When using such a sequence in MR tomography corresponding to the RARE method, the contrast of the image is essentially given by the intensity of the echo which represents the center of the k space in the phase encoding direction.
In a preferred implementation of the inventive method, it is therefore reasonable to recover complete refocusing for exactly this echo. Towards this end, in a first approximation, the signal intensity of the image becomes independent of xcex11 . . . xcex1n. Selection of xcex11 . . . xcex1n less than 180xc2x0 only slightly changes the sharpness of the image. It is advisable thereby to chose values for xcex11 . . . xcex1n which generate a possibly high and homogeneous echo amplitude as described e.g. in (D4) and (D5).
In particular, for so-called multi-contrast methods wherein phase encoding is carried out such that at least the center of the k space is read several times and at different echo times, the principle according to equation [12] can be repeated several times even during an echo train such that several hyper-echos can be formed in one echo train.
The chosen example of application to a RARE sequence merely has illustrative character. Hyper-echos can be integrated also in other imaging sequences such as GRASE, BURST etc. to improve the signal behavior through refocusing of magnetization.
2. Driven Equilibrium Sequences
A further particularly preferred application of the inventive method deals with recovery of z magnetization in so-called driven equilibrium (DEFT) sequences. Application of DEFT to spin echo sequences for MR imaging was described already in 1984 (D7). It is based on the application of a so-called flip back pulse at the time of echo formation, i.e. when all transverse magnetization is refocused. This flip back pulse converts the remaining transverse magnetization into z magnetization. Same is thus closer to the thermal equilibrium which achieves higher signal intensity with identical recovering time.
In a hyper-echo sequence, such conversion of the spin system in the direction of balanced magnetization can be realized in two ways: If the entire sequence is designed according to the principles of hyper-echo formation and applied to z magnetization, magnetization at the time of hyper-echo formation according to [11] will be z magnetization. Same can be converted into z magnetization through a directly following 180xc2x0 pulse (FIG. 4A). The same effect can be achieved if the 90xc2x0 pulse is phase-inverted at the end of the hyper-echo sequence thereby acting as a flip back pulse which converts magnetization directly into +z magnetization (FIG. 4B).
RARE (TSE . . . ) sequences having small refocusing flip angles (see above) permit rotation back to the z axis only of part of the magnetization by means of a flip back pulse due to incomplete refocusing. Application of the inventive method, however, allows regaining of the entire transverse magnetization through formation of a hyper-echo for the time of the flip back pulse and conversion into z magnetization through flip back.
This application is mainly (but not exclusively) useful for application in high field systems wherein on the one hand, often small refocusing flip angles are used due to the increased radio frequency absorption, and furthermore long repeating times are required due to the generally longer T1 relaxation times with increasing field strength without flip back to balance out magnetization as well as possible before the next excitation.
The method is thereby particularly preferred for applications which offer an inherently short repeating time, such as e.g. recordings with three-dimensional local encoding or rapidly repeated recordings for observing temporally changing processes.
It is also possible to refocus gradient echo sequences through hyper-echo formation by introducing a 180xc2x0 pulse into the sequence after reading out m excitation intervals, in which one gradient echo is generated in each case, followed by further m excitation intervals with pulses corresponding to equation [11]. FIG. 5A shows a hyper-echo sequence based on a gradient echo sequence. Therein, the temporal succession of the entire sequence was converted after the 180xc2x0 pulse and the pulses were changed corresponding to [9]-[11]. To simplify matters, FIG. 5A shows a sequence with constant flip angle xcex1. Taking into consideration equations [9]-[11] hyper-echo formation is effected also for sequences with variable ox.
As shown, the signals recorded in the second half of the sequence correspond to the signal parts refocused by the 180xc2x0 pulse. Since the symmetry condition for the hyper-echo formation holds true merely for the entire spin dephasing between two subsequent radio frequency pulses in each case, the sequence shown in FIG. 5B also leads to hyper-echo formation. In contrast to FIG. 5A, in this case, merely the read gradient GR was temporally inverted (and the slice selection gradient GS was made symmetrical) such that now, the gradient echos directly generated by the respectively preceding radio frequency pulse, were formed also in the second half of the sequence. Considering [9]-[11] with respect to total dephasing between the pulses, a hyper-echo is also formed in this case.
Suitable selection of the gradients allows reading out of both possible signal groups (FIG. 5C). Same may either be generated and read separately. When the reading gradient GR is designed such that the entire surface below GR between 2 refocusing pulses becomes zero, these signals overlap to form one single signal corresponding to the principle of the FISP sequence.
The measuring methods shown in FIGS. 5A-C can be carried out either such that the signals used for imaging are recorded in one single hyper-echo train. This can be carried out also such that a data set required for image construction is achieved only after multiple repetition of the corresponding sequences. In particularly preferred implementations, inversion of the initial z magnetization caused by hyper-echo formationxe2x80x94as already shown in the multi-echo method in FIG. 4xe2x80x94is inverted before the recovering time through a 180xc2x0 pulse and thus brought closer to an equilibrium (FIG. 5D).
It should finally be noted that formation of several hyper-echos is possible also for gradient echo sequences (FIG. 5E).
When the excitation pulse is started with a flip angle of generally, but not necessarily 90xc2x0, the hyper-echo can also be formed as signal with transverse magnetization (FIG. 5F) which can again be converted into z magnetization corresponding to the description for multi-echo sequences through a flip back pulse (FIG. 5G) before the recovering time tr. In the variants shown in FIGS. 5D-G, the generic sequence (FIG. 5A) was taken as a basis but also the variants corresponding to FIG. 5B,C (inclusive FISP) can be used.
To optimize steady-state magnetization in continuous methods such as FIG. 5E, it may also be useful to realize the initial excitation pulse and the refocusing pulse used for hyper-echo formation not as pulses having a flip angle of 90xc2x0 and 180xc2x0 but as pulses with correspondingly smaller flip angles xcex2 (excitation) or 2xcex2 (refocusing), wherein the phase of the refocusing pulses alternates with repeated application according to the principle of a true FISP sequence.
Hyper-echos can be integrated also in other imaging sequences, such as echo planar imaging, spiral imaging etc. to modify the contrast behavior e.g. corresponding to the formation of the driven equilibrium.
The application, as described, onto measuring methods in MR imaging are merely illustrative. A large number of measuring sequences in analytical NMRxe2x80x94mainly multiple-dimensional Fourier spectroscopyxe2x80x94such as COSY, NOESY, INEPT, INADEQUATE etc.xe2x80x94to name only some of the current sequences, is based on a plurality of repetitions of multi-pulse sequences. With all these sequences, balanced magnetization can be achieved more rapidly through formation of a hyper-echo with subsequent flip back pulse and thus reduction of the measuring time and/or increase of the signal-to-noise ratio. If in such sequences, pulses are applied to different nuclei, formation of hyper-echos onto all nuclei concerned is advantageous.
The use of hyper-echos in driven equilibrium sequences is particularly advantageous mainly for observing nuclei with long T1 since in this case, magnetization with a suitable sequence (e.g. imaging) can be read and subsequently re-stored as z magnetization to be read out again at a later time.
A preferred application in this case is the measurement using hyper-polarized magnetization (e.g. through corresponding preparation of hyper-polarized inert gases). Therein, the longitudinal magnetization is prepared in a state far beyond from the thermal equilibrium. The prepared spin system thus produces a signal intensity which is in factors of several thousand above that of the balanced magnetization. Such hyper-polarized substances are applied e.g. in MR tomography using hyper-polarized helium for illustrating the lung. A problem produced in this connection is that magnetization, once it has been excited, relaxes into the balanced state and thus loses polarization. The use of flip back sequences allows regaining of the polarized magnetization without the relaxation losses caused by T2 and can thus be re-used several times.
3. Spin Selection
Hyper-echo sequences may be used for selecting a sub-amount of the originally excited spins if modification is carried out such that the symmetrical condition of equation [11] leading to hyper-echo formation is fulfilled only for part of the spin. A large number of such applications can be derived from the plurality of sequences known in NMR literature which can be described only illustratively and not completely below.
3.1. Spin Selection Through Variation of Symmetrical Conditions for Hyper-echo Formation
Spin selection in a hyper-echo experiment can be realized by selecting the pulse sequence such that the symmetrical conditions of equation [11] are met only for part of the initially excited spins. This can be achieved e.g. with application of slice-selective pulses in that the individual pulses act in each case only onto spins within a certain frequency range through selection of corresponding pulse profiles. With corresponding selection of the respective frequency ranges, it is possible to filter out signals from a partial range of the excitation profile of each pulse. With simultaneous application of magnetic field gradients during the pulses, one can observe spins from corresponding spatial volumes.
FIG. 6 shows in this connection a simple example of application, wherein the profiles of the corresponding pulses which are symmetrical with respect to the central 180xc2x0 pulse are displaced with respect to one another such that hyper-echo formation is effected only in the overlapping central spectral range (grey) whereas the signals of the outer regions appear to be dephased depending on phase and flip angle of the pulses.
A particularly effective type of this hyper-echo formation results when the phase of the pulses 1 . . . n is continuously alternated since spins in the outer regions are submitted only to the pulses with the identical phase used in a Carr-Purrcel sequence which is known to produce a rapid signal loss and thus signal suppression for xcex1 less than 180xc2x0.
Other implementations are also possible which have the common feature that the condition for hyper-echo formation is fulfilled only in the region of the desired excitation window. A particularly simple implementation can be achieved also in that merely the central refocusing pulse has a different selectivity (e.g. chemical shift selectivity) with respect to the other pulses of the hyper-echo sequence.
A generalization of this principle is schematically shown in FIG. 7, which shows that a complex excitation window can be obtained through application of a pulse sequence with simple excitation profiles.
Spin selection is also possible through modification of the temporal order of the pulse sequence before and/or after the central 180xc2x0 pulse through an additional modulation step E(xcfx86E). In case of introduction before the central 180xc2x0 pulse, the effect of the pulse sequence is then according to equations [9]-[11] described as
xe2x80x83MR(Mx,My,Mz)=R(xcex11,180xc2x0xe2x88x92xcfx861,xcfx861) . . . *R(xcex1nxe2x88x921,
180xc2x0xe2x88x92xcfx86nxe2x88x921, xcfx86nxe2x88x921)*R(xcex1n, 180xc2x0xe2x88x92xcfx86n,xcfx86n)*R(
180xc2x0,0,0)*
E(xcfx86E)*R(xcex1n,xcfx86n,xcfx86n) . . . *R(xcex12,xcfx862,xcfx862)*R
(xcex11,xcfx861,xcfx861) MA(Mx,My,Mz)xe2x80x83xe2x80x83[14].
Hyper-echo formation occurs only for that part of the spins for which magnetization remains unchanged, corresponding to the vectorial disintegration, this is MRCOS(xcfx86E). The corresponding orthogonal component Mxe2x80x2R xe2x80x9cseesxe2x80x9d pulses which are phase-shifted by 90xc2x0 after the interval E(xcfx86E) and therefore develops:
Mxe2x80x2R(Mx,My,Mz)=R(xcex11,90xc2x0xe2x88x92xcfx861,xcfx861)*R(xcex1nxe2x88x921,90
xc2x0xe2x88x92xcfx86nxe2x88x921, xcfx86nxe2x88x921)*R(xcex1n,90xc2x0xe2x88x92xcfx86n,xcfx86n)*R(180xc2x0,90xc2x0
,0)*
E(xcfx86E)*R(xcex1n,xcfx86n,xcfx86n) . . . *R(xcex12,xcfx862, xcfx862)*R
(xcex11,xcfx861, xcfx861) MA(Mx,My,Mz)xe2x80x83xe2x80x83[15].
With corresponding selection of xcfx861 . . . xcfx86n, this signal portion is suppressed. In the most simple case, this can be achieved for xcfx861 . . . xcfx86n=0xc2x0 and xcex11 . . . xcex1n less than 180xc2x0.
If E is represented as an additional time interval td (FIG. 8A) the symmetry of the hyper-echo sequence for resonant spins is not disturbed. Spins having a certain off-resonance frequency xcfx89 greater than 0 experience in contrast thereto a phase change xcex94xcfx86 corresponding to xcex94xcfx86=xcfx89td. Same causes distortion of the symmetry of the hyper-echo sequence and the signals of said spins are suppressed. E(xcfx86E) may also be designed much more complex.
FIG. 8B shows as further example introduction of an additional spin echo interval with symmetrical strong magnetic field gradients. Moving spins are dephased by these gradients. When all spins move uniformly as in vascular flow, this leads to velocity-dependent phase changes of the observable magnetization which impairs the symmetry condition of hyper-echo formation and thus causes attenuation of the hyper-echo signal.
Spin ensembles which move incoherently due to molecular diffusion experience an amplitude change due to the incoherent dephasing, which depends on the diffusion constant and will also attenuate the amplitude of the subsequent hyper-echo. Formation of the hyper-echo per se will not be influenced by diffusion.
In a conventional spin echo sequence, spins moving at a constant velocity are represented without signal loss but with altered signal phase. In a hyper-echo sequence, in which the signal portion Mxe2x80x2R(Mx,My,Mz) represented in equation [14] is dephased and therefore does not contribute to the total signal, phase effects do not occur.
Change of the signal phase depending on the motion and thus loss of the hyper-echo formation will occur merely through switching a bipolar magnetic field gradient by one (or several) of the refocusing pulses with otherwise constant time scheme (FIG. 8C).
The embodiments shown in FIGS. 8A through 8C of a modified hyper-echo sequence are again exemplarily. Literature (see e.g. (D9), (D10)) shows a large number of method steps which include concrete change of the signal phase and/or amplitude and can be applied also in a hyper-echo sequence.
It is to be noted that all modifications which, when applied to conventional spin echo or gradient echo sequences, lead to phase change, effect a signal intensity loss in the hyper-echo formation. Phase effects will depend on the fate of the magnetization component orthogonal to that leading to hyperecho-formation.
3.2 Hyper-echos for Suppressing of Signals of Coupled Spins
As initially mentioned, hyper-echo refocusing according to equation [11] is true for mechanisms, such as chemical shift, susceptibility etc., i.e. spin states which are characterized by a temporal development of the phase and which are inverted by a 180xc2x0 pulse. Other mechanisms such as zero and multiple-quantum coherences and J-coupling show a different refocusing behavior and thus do not follow the same conditions for hyper-echo formation.
On the other hand, following the general symmetry relations described in Eq.[1]-[5] can also be applied to such mechanisms, such that a hyper-echo is then selectively formed for coupled systems, however, not for uncoupled spins. Corresponding selection of xcex1n, xcfx86n, xcfx86n, permits discrimination of the corresponding spin states.
Some typical applications for coupled spins are exemplarily shown below. This representation, too, is only exemplarily and not complete. Further applications for other states such as zero and multiple quantum coherences can be easily derived from the basic equation [11].
Spin systems comprising J-coupling have a different refocusing behavior than coupled spin systems which is shown by an AX system below. Extension to other systems is easily possible. An AX system is characterized as weakly coupled system wherein the difference of the chemical shifts of the A and X nuclei is larger than the coupling constant J. Such a system is characterized by two doublets. If a refocusing pulse is applied to such a system, magnetizations are refocused on the one hand and on the other hand, the corresponding coupling partners are simultaneously exchanged which means that after this double inversion, the spin system behaves with respect to J-coupling as if no refocusing had taken place.
When refocusing pulses having a flip angle of exactly 180xc2x0 are applied, this causes that the phase of the echos of coupled spins develops differently than that of uncoupled spins. This is the basis of methods such as COSY etc.
When several pulses are applied which have a flip angle other than 180xc2x0, this phase development causes increasingly destructive interference and thus signal loss. In particular, with CPMG sequences, there is a positive interference loss of the different signal contributions corresponding to ref. (D3) if the pulse separation with respect to J and xcex94"sgr" is sufficiently large (D8). It is therefore possible to suppress the signals of coupled spins through a corresponding multi-pulse sequence. Although the principle is known, such a method is not often used in practice since the required condition of using flip angles  less than 180xc2x0 leads to signal loss of the observed uncoupled spins and this method is disadvantageous compared to other discrimination methods.
In contrast thereto, a sequence which forms a hyper-echo with respect to the signals of uncoupled spins results in full signal intensity, whereas signals of coupled spins are suppressed since they effectively xe2x80x9cseexe2x80x9d another phase of the refocusing pulses. Towards this end, we observe such a doublet signal and assume that the reference frequency is in the center of the doublet. The doublet signal will then experience a phase development according to cos(J/2*tn) wherein tn is the time after excitation (FIG. 9).
A particularly advantageous feature of this application is given in that with corresponding selection of xcex1n, xcfx86n, xcfx86n signals of spins of systems having different coupling constants can be simultaneously suppressed.
Suppression of the signals of coupled spins is prevented by selecting the time of the central 180xc2x0 pulse=1/J (FIG. 9 below). This is true, of course, only for spins having particular coupling constants J.
This principle of different phase development can be also used for the reversed purpose of specifically selecting coupled spins. This is achieved in that the phase development according to J-coupling in the phases on of the refocusing pulses is taken into consideration. Modification of a hyper-echo sequence according to equation [11] leads to incrementation of each pulse phase xcfx86n about arcsin(J/2*tn) and shows that formation of a hyper-echo can be achieved only for the corresponding signal whereas for signals with different coupling constants and also for signals with uncoupled spins, the symmetry relation according to equation [11] is not met and same thus appear attenuated, wherein already a few refocusing pulses achieve attenuation leading to a practically complete suppression of said signals.
Corresponding to this simple example, a large number of pulse sequences can be devised which have the same feature, i.e. that the symmetrical relation for hyper-echo formation is met in each case only for the spins to be observed, however not for others. This is true in particular also for zero and multiple-quantum coherences for which a hyper-echo method with corresponding selection or suppression of the differently associated signals can be easily derived from the description with respect to J-coupling.
The observation that when the symmetry of the phase development according to the above chapter 3 is not fulfilled, only the cosine contribution of the magnetization contributes to the hyper-echo formation, there is the possibility of using the hyper-echo formation as polarization filter which allows passage only of signals with a symmetry following the hyper-echo sequence and deletes the signal contributions which are orthogonal thereto. Application of several such polarizations, optionally with selection under different polarization angles, permits specific selection of signals whose dephasing follows corresponding and precise handicaps.
4. Spin Inversion
Application of a sequence according to equation [11] to pure z magnetization leads to spin inversion as used for so-called inversion recovery sequences for T1 measurements or also in the field of imaging for achieving T1 weighted images. Application of a hyper-echo sequence in contrast to conventional inversion with one single 180xc2x0 pulse thereby permits use of methods for selective spin inversion described under chapter 3. On the one hand, one can obtain complex inversion profiles, on the other hand, selective inversion corresponding to chemical shift, J-coupling, different zero and multiple-quantum coherences etc. is possible.
Considerations for Implementation
In implementing hyper-echoes, one has to differentiate that formation of hyper-echos can be integrated either in the course of the measurement with a certain pulse sequence which is advantageous mainly for the sequences mentioned above in chapters 1 and 2. Implementation is also possible or even advantageous, wherein formation of a hyper-echo initially serves for special preparation of the spin system, and data acquisition is carried out subsequently using any appropriate sequence (according to FIG. 2D).
The acquisition module can thereby be formed from any appropriate signal generation sequence. Mainly in applications in MRtomography, the acquisition module may consist of a corresponding imaging module (gradient echo, echo planar imaging, RARE(TSE, . . . ) spiral scan etc.) such that images are produced which have a contrast which corresponds to the characteristic of the hyper-echo.
There are further applications wherein hyper-echos are used in a different context than up to now. Literature discloses (D3) that in multi-pulse sequences, a number of possible refocusing paths for transverse magnetization, which increases with the 3rd power of the number of pulses, is generated of which often only part is used to contribute to signal read-out. When such a sequence is repeated with a repetition time which is smaller than the longitudinal relaxation time T1, undesired signals may be formed which can be prevented through hyper-echo formation since thereby all refocusing paths are combined again. Such a xe2x80x9cclean-upxe2x80x9d function may be reasonable in particular also when using NMR in quantum computing since hyper-echo formation can serve here as deleting function of the information stored in the spin system as transverse magnetization.
Further advantages of the invention can be extracted from the description and the drawing. The features mentioned above and below may be used in accordance with the invention either individually or collectively in any arbitrary combination. The embodiments shown and described are not to be understood as exhaustive enumeration but rather have exemplary character for describing the invention.
The invention is shown in the drawing and is further explained by means of embodiments.